BEAUTIFUL UNIVERSE

2. CONCEPTS
IN 20th. CENTURY PHYSICS RE-EXPRESSED IN
TERMS OF BEAUTIFUL UNIVERSE THEORY

2.1
GENERAL NATURE OF THE (BU) THEORY

An
attempt will be made in the following sections to
outline qualitatively how some basic Newtonian, (SR), (GR) and (QM)
concepts can
be ‘reverse engineered’ – i.e. their results are first separated from
their original
theoretical and mathematical frameworks, then reconstructed using the
premises
and interactions of (BU) theory.

While
(BU) theory is causal and local, it is not classical, since no
continuous
integral processes are possible: the nodes are discrete with units of
action h,
and other than the spin of individual nodes in situ, absolutely
nothing
else actually moves. Unlike classical theories, no preconceived ideas
about mass
or motion are used, but these concepts are developed from first
principles. Assuming
neither flexible spacetime nor the constancy of the speed of light, the
theory
is not relativistic (SR) or (GR) either. The speed of light is the
maximum
speed between nodes, so a simple Galilean relativity does not apply.
There are
no inherent time and space dimensions in (BU), but to aid keeping track
of the
changes of the state of the universe, a fixed time dimension can be
defined as
described above. Even so, this time dimension should not be
thought of as a
standard universal time zone, since all interactions are measured
locally, and
signals from various distances arrive at various times relative to
their
distance and velocity of the source. Three fixed space dimensions
can be
defined from the geometry of the nodes, but again such directions are
not
absolute in the universe as a whole. Nor does (BU) depend on
concepts
of probability so it is not a variation on (QM) in its Copenhagen
interpretation.

A
curious aspect of (BU) is that concepts that were simple in classical
physics
becomes complex, while (SR) and (GR) on the other hand become simple.
Motion, which
was considered a simple change of position of a whole mass in time, now
involves
the complex process of self-convolution. This involves all the nodes
making up
the mass as well as those in its own gravitational field in which it is
moving.
Conversely, (SR)
and (GR) can be derived simply from the model without using complex
equations
of differential geometry to describe a physically unrealistic flexible
spacetime dimension. There are the usual relativistic effects in (BU)
but they can
be derived from the model using classical concepts. Similarly the
results of (QM)
can be re-formulated on the basis of the electromagnetic waves
transferred
within a field of nodes. It is speculated that only two basic
constants co and h are necessary to describe nature, and that all other constants,
including
the constant of universal gravitation G can be derived from them.

If
these expectations are confirmed, then all the laws of physics can be
derived systematically
and quantitatively from the handful of a priori premises of
(BU),
revised as necessary. If successful, this would be the basis of a
unified
theory of physics. Such a systematic ‘theory of everything’ (TOE)
is too
ambitious a task for this speculative paper and will be left for future
work if
the (BU) concepts are found feasible.

2.2 A DISCRETE
CALCULUS FOR (BU)

The
reductionist nature of BU demands matching mathematical methods. Newton
developed
the calculus to describe concepts such as acceleration. Einstein
adapted the
language of differential geometry and tensors to describe his notions
of
flexible space and time. No new or difficult mathematics is
necessary to
describe (BU) interactions. The node structure in (BU) resembles
that of 3-dimensional
arrangements of atoms in crystals or metals, so some of the
well-developed
notation to describe the various orientations of facets[40] might be useful in developing (BU) interactions. Unlike crystals
however, (BU)
has no free electrons transporting electricity or diffusing heat, so
this
comparison should not be taken too far.

Rather,
in (BU) a field or action is described by a summation of discrete
intervals or stepwise
changes. The summation symbol ∑ of discrete calculus [41]now
appears instead of the integeral .
It is only on the
scale of relatively large distances on the atomic or molecular scale
and larger
that the incremental nature of BU can be ignored, and phenomena can
then be
treated with continuous integrals. Continuous integral fields only
apply when
the Xmax the maximum physical dimensions considered are much
larger
than the node-to-node distance do. A scaling factor Sc is
proposed to judge when (BU) interactions warrant a discrete treatment.

(15)

An
interaction would be quantum in nature if Sc is, say,
between zero
and one, and classical for larger values. (BU) functions are complete
in
themselves, but for the sake of comparison with current models, they
may be
regarded as a regular sampling[42] at the nodes of such continuous functions. In (BU) there is no
conflict
between descriptions of the macroscopic world of large objects and the
quantum world
(FIG. 21).

If
each node is given a label axyz then the very geometry of
the
lattice resembles a sort of matrix, and matching mathematical matrices
can be
developed to describe various interactions. It will be discussed in
section 2.7
how Heisenberg’s matrices in QM might be derived from this geometry.
Similarly
the tensors of general relativity describing the local deformation of
spacetime
can also be reinterpreted within (BU), using the moments of the nodes
to define
local density.

Since
there is no space between the nodes, a signal travels between two nodes
A and B
within a volume of space in (BU) only via the network of intervening
nodes. A
‘straight line’ will actually be a jagged zigzag of segments, not a
smooth
diagonal crossing over an infinitely divisible space. The total
path length
of, say a ray of light, will be larger by a factor of 1=<FL =<√3
depending on the direction of the line within the cubic lattice in
three
dimensional space. For example, in the case of the line AB in Figure
21(c), aligned exactly diagonally across the cubic lattice, FL =√3 .

FIG. 21. Discrete Calculus in (BU). (a) A
function in
the x-y plane of a volume of nodes centered on an arbitrarily chosen
node (0)
is described by summation functions ∑ showing discrete quantum behavior
from node to node. The maximum function value Xmax is of the
same order
of magnitude as the node-to-node distance do. Distances are
not
measured in straight lines such as OC, but along zigzag paths
connecting the
nodes. (b) In macroscopic systems in (BU), Xmax>>do and the
same function can be described by integrals (c) Multiple paths
are
possible from node A to node B in a two or three dimensional volume of
space.

Vectors
too will describe zigzag paths on the scale of the nodes. A macroscopic
vector
from any node A to node B will be identical to the summation of smaller
node-to-node
vectors starting from A along any path or paths to B. This concept is
useful in
expressing treatments such as Feynman’s sum over histories[43] of an interaction.

Another
significant aspect of (BU) is that functions such as the gravitational
potential
containing inverse distances never explode into infinity as in the case
of (GR), because
in (BU) a distance can never be zero, i.e. less than do.

2.3
AN ETHER TO CARRY ALL INTERACTIONS

(BU)
is a new type of ether theory, a substance that was supposed to fill
all of
space and argued over since antiquity[44].
The crucial difference between (BU) and earlier concepts of ether is
that in
(BU) everything is made up of the ether. The distinction
between solid
matter, energy, and empty space that has confused most of the earlier
theories
does not occur in (BU). Descartes had speculated that light is
transmitted in
space by the action of tiny vortices[45] (FIG 22), not too different from the nodes of (BU).

FIG. 22 Descartes’
vortices

FIG. 23 The ether mechanism envisioned
by J. C. Maxwell in 1861

Thomas
Young theorized that diffraction of light is due to
its refraction in a dense medium adjacent to matter[46].
Faraday assumed the existence of lines of force in space to carry
magnetic effects.[47] At one time Maxwell[48] had assumed such a mechanical model of an ether for his electromagnetic
field,
and imagined a system of gears surrounded
by
particles interacting together to carry the field along (FIG.
23).

When
Michelson and Morley’s experiments[49] showed that light is not retarded by its passage through a supposed
ether, it
caused a crisis in physics. How was light transmitted? Thompson
(Lord Kelvin)[50] was a firm believer in the ether, and that atoms were knots in it. As
the
discoverer of the electron he believed that both atoms and the ether
were
electrical vortices, but failed to translate this idea into a complete
theory. It
is interesting that recent topological researches now show that aspects
of knot
theory are closely linked to gauge fields and gravity[51] and to
quantum
field theory [20]. By adopting
the two postulates of the constancy of the
speed of light
in a
flexible space and time, and the principle of equivalence of all
inertial
frames, Einstein’s (SR) succeeded in describing the electrodynamics of
moving bodies
without recourse to the concept of an ether. The ether seemed to have
evaporated
forever.

Ironically
it was Einstein himself who lectured in 1922 on
the need for an ether[52],
some years after the results of (SR) and (GR) were experimentally
proven. He
needed a medium to carry his mesh of ‘clocks and measuring rods’. In
1954 Dirac
said “...the failure of the world’s physicists to find such a
(satisfactory)
theory, after many years of intensive research, leads me to think that
the
aetherless basis of physical theory may have reached the end of its
capabilities and to see in the ether a new hope for the future.” [53].
Recently there has been speculation that the fifth dimension in the
Kaluza-Klein
solution[54] for Einstein’s equations is a lattice of ether nodes.

In
the second half of the 19th Century it was discovered that
Maxwell’s
equations failed to account for events in frames of reference moving
relative
to each other. Soon afterwards Heaviside[55],
Fitzgerald, Lorentz [56]and
Poincare, put forward various classical theories proposing length
contraction
and time dilation to correct problems in applying Maxwell’s equations
in moving
frames of reference, and to explain why such transformations make it
impossible
to detect the ether.

Unfortunately
instead of extending these earlier results, Einstein
chose to recast them using a mathematically equivalent model. He
proposed,
without relying on any experiment or observation from nature, that it
is space
itself that contracts, and time itself that dilates in a
moving frame;
not merely the length of the measuring rod, and clock time used by an
observer
in a relatively moving frame. This allowed him to assign a fixed velocity of light c=contracting space / dilating time. Einstein’s
arbitrary postulates imposed an elegant abstract unity in the laws of
physics,
which then become independent of frames of reference, but at the
cost of a loss
of physical realism. This does not belittles his lasting contribution
in (SR) 8 : that
electromagnetic radiation with a maximum velocity of c has a
fundamental role
in defining space and time. FIG. 24 compares the concept of

(SR)
with its multiple moving frames of reference, to a realistic frameless
universe
where meaningful physical events only occur locally at the smallest
scale
possible.

FIG. 24. Special and General Relativity
describe the motion
of bodies with a separate frame of reference for each moving object.
Within
each object a spacetime grid is distorted differently according to its
motion
(arrows). Beautiful Universe Theory describe such motions within a
regular fixed
lattice geometry made up of nodes of varying energy and orientation
exchanging
momentum locally, simplifying the description.

In
(BU) the results of (SR), but not its premises, can be adapted
from any of the many and various available classical derivations
of the
Lorentz transformations, the earliest being Heaviside’s55 analysis of how a sphere of charges contracts in the direction of
motion to
become an ellipsoid (FIG. 25). Of course it is not the individual
nodes
themselves that change shape, but the energy pattern they define in the
lattice. LaFreniere[57] explains length contraction in classical fields as a consequence of
a Doppler
shift in electron spherical standing waves making up matter.

FIG. 25. The Heaviside Ellipsoid. A
spherical
arrangement of charges will contract in the direction of its motion to
become
an ellipsoid. In (BU) this will be the simple consequence of a Doppler
shift in
the de Broglie electron standing waves making up an atom.

Heaviside concluded
that a charge moving at a velocity v is equivalent to an electric field
following the form:

(16)

where E is evaluated at a point
with displacement r from the center of the charge distribution and q is the angle between r and the
direction of
motion. The length contraction in (BU), however, is a combination of a
‘real’
contraction combined with the effects of a contraction due to measurement from an outside frame. Because of Heaviside contraction, the
number of nodes the
matter spans lengthwise during its motion is smaller than those when it
is
stationary. An outside observer then attempt to measure this
length of a
moving body for example by sending light signals to mirrors attached to
the
front and the back of the body, and comparing the signal arrival times.
Because
of a Doppler shift in these signals, the frequency increases, and this
is equivalent
to a time dilation. In (BU) it is these physical effects of length
contraction
due to the compression at impact, multiplied by the dilation in the
timing
factor that should explain the (SR) length contraction.

Similar
‘physical’ arguments about the gain of mass of a
moving body can be made in (BU): it is just the momentum added to its
internal
energy upon impact that affects this increase. Using the classical
Lorentzian
transformations featuring, the
mass, length and measured
clock time of a body ‘moving’ at a velocity v= cs= c0 /n can
be derived
in (BU). The body’s energy pattern is transmitted across the lattice at
a
velocity v. And as we have seen, is a fundamental property of node, its potential energy or ‘density’,
whether
the node is found within matter, in a radiation field, or in empty
space.

A
useful way to analyze the (SR) transformations in (BU) is
the following. The cores of atoms are an assemblage of locked nuclear
matter whose
size is insignificant, as compared to the overall size of the atom’s
outer
shells, defined by the electrons oscillating in standing de Broglie
waves[58].
When an
inelastic force impinges on
matter, forward
momentum is added to it, which travels like a wave from node to node.
The spherical
standing waves making up the shells are compressed into Heaviside
ellipsoids
and the energy pattern is transferred within the object in this
contracted form,
until the force’s momentum is expended. This can be
developed into a
formalism whereby a force F of nodes with forward momentum first causes
the
contraction of the stationary object it collides with. Then, after the
stationary object contracts, it moves forward with a velocity v. This
links Newton’s
ideas of force and motion with the Lorentz transformation of length.
These
effects appear in the abstract formulation of (SR) because length
contraction
actually occurs in nature, as explained in (FIG. 26). Similarly the
(SR) effect
of time dilation is explained as an actual delay in the time of arrival
of
light signals used by an outside observer, in the act of measuring the
length,
once the body starts to move.

FIG. 26. Force, Momentum, Motion and Lorentz
transformations. At time to momentum arrives as a force F on
a
molecule made up of four atoms of length Lo (circles, at
bottom). The
momentum is absorbed and two of the atoms are contracted into Heaviside
ellipsoids
(middle). By time t1 all the momentum has been absorbed by three atoms
(top).
The Lorentz contraction is Ls and the final length of the molecule is
Lv. At
time t2 the entire contracted molecule starts its motion at
a velocity
V. Anytime after t2 an outside observer from a fixed point O
attempts to
measure the length of the molecule by sending light beams (dashed
lines) to attached
mirrors. The Doppler-shifted times of arrival of the light are
equivalent to a
time dilation, and the estimate of length Lv is further contracted.

The
second unique contribution of Einstein in relativity
theory was his discovery of the equivalence of gravity with
acceleration, a
result admired by Lorentz himself. Again Einstein used the
concept of flexible
spacetime to describe the resulting deformations, using complicated
tensor
mathematics. Eddington, who proved (GR) experimentally by measuring the
predicted deviation of starlight by the sun’s gravity, hinted that GR
could be
explained in simple classical terms: Eddington argued that gravity
affect the density
of space, causing its index of refraction (n) to increase and what he
called
the ‘coordinate velocity’ of light to slow down[59].

In
the (BU) model the strength of the gravitational field
is described by nxyz the local relative ‘density’ of the
nodes. As (n)
changes from node to node, the velocity of signals there changes- i.e.
signals accelerate as (n) changes. In this way (BU) provides a physical explanation
for the famous
equivalence of gravity with acceleration in GR. A description of
signals in
such a field of variable n reduces to the Hamiltonian Analogy[60],
an enduring idea mentioned by Ibn Al-Haytham (Hazen) in the 10th Century,
that the path of a particle in a potential field resembles that of a
ray of
light traveling in a medium of variable index of refraction[61] (FIG. 27). The Analogy was systematically developed in the 18th Century
by Hamilton[62], [63]who
posited that a particle’s energy is always constant made up of variable
potential and kinetic energy

(17)
E
= P.E. + K.E

an
equation known as the Hamiltonian. In (BU) P.E. is the node’s internal
energy,
its spin, while its K.E. is its forward momentum, i.e. how it affects
its immediate
environment. In optics the eikonal equation[64] relates (n) to the potential:

(18)

FIG. 27. The Hamiltonian Analogy in (BU).
Variable potential
energy (indicated by the shades of the nodes) implies that volumes of
space transmit
node-to-node signals at different velocities and will have different
indices of
refraction (n). The laws of geometrical optics then apply to both
radiation streamlines
(S) and the paths of moving particles (P). Along these paths the
transmitted energy
is constant, equaling the potential energy plus the kinetic energy at
any given
point. (a) Snell’s law applies to a geodesic crossing an interface
between a
field of energetic (i.e. dense) nodes of index of refraction n1 to
one with n2<n1. (b) A dipole field
has a radial
distribution of n causing streamlines S to curve in circular paths. A
particle
crossing this field curves accordingly. (c) A Schwarzschild metric for
the
gravity of a particle at the center, is interpreted in (BU) in terms of
local
density variations without invoking spacetime distortions. The
curvature of a
geodesic (P) for a particle is similar to the bending of light passing
through the
dense gravitational field of a star.

In
electromagnetic fields the paths along which the energy is
transmitted (normal to the equipotential surfaces) are the streamlines
S. According
to (GR) test particles in a potential field always travel along
straight-line
geodesics in a curvedspacetime. In classical physics
and in (BU),
and in accordance with the Hamiltonian Analogy, an inhomogeneous
gravitational
potential causes light and test particles to accelerate along curved
streamlines S in ‘straight’ space and time coordinates. This agrees with
Euler’s result
relating acceleration a=dv/dt with a change in curvature, d/dt . Accelaration can also be expressed as in Eq. 19 .

(19)

Using a result from optics, the curvature k can also be expressed in terms of the index of refraction n

(20)
k= n grad log n

Where n is the unit normal to the equipotential (ie tangent to the streamline S orthogonal
to it) at a
point in the field. The description above should yield the same results
as (GR),
except that in (BU) the physical situation would be much simpler,
merely
requiring an iterative incremental linear solution of Snell’s law for
the
deflection of light in adjacent media of different indices of
refraction. This
was demonstrated by Tamari[22] for a simple dipole field. These effects are linear in (BU), and can be
applied
numerically to any configuration of matter, however complex its shape,
inhomogeneities
in its composition, or a mixed pattern of motions (linear, rotational,
etc.) of
its various parts. This is in contrast to (GR) where solutions to
Einstein’s complicated
tensor equations are only known for a few simple cases such as a
sphere.

(BU)
also provides a physical explanation of why there is
no dipole solution for Einstein’s (GR) equations, while solutions exist
for quadrupoles
and higher terms: The smallest piece of matter in (BU) is made up
of two nodes,
each node being a dipole. Two adjacent dipoles make up a quadrupole.

The
Hamiltonian operator, which is related to (Eq. 17) is a
fundamental part of Schrödinger’s Equation[65] , the basis of (QM), reinforcing the belief that in (BU), (GR) and (QM)
can be
unified in a single theory. Conversely it should be possible to derive
Schrödinger’s equation in (BU) by equating the mass of a particle with
the total
momentum (in multiples of (h)) of the nodes it is made up of, and
considering
their mutual interactions as standing spherical waves in the shell of
an atom.

Maxwell’s
equations can be derived directly in (BU) from the fact that along the
streamlines in free space the electric and magnetic effects generated
by each
node propagate as a sinusoidal wave at a velocity c0/n.
along
streamlines S. Maxwell’s continuity equation can also be derived
directly because
the energy transmitted along any given streamline is a constant. A
small volume
of space which encloses a bundle of such streamlines transmits equal
amounts of
current in and out of that volume. Maxwell deduced the velocity
of
electromagnetic radiation c0 from the square root of the
permittivity of free space divided by its permeability. In (Eq. 4) the
vacuum node’s
spin in units of (h) decides the speed of propagation c0,
suggesting
a relation between all these quantities.

2.6
NO DUALITY IN (BU): THE PHOTON IS A WAVE
PATTERN OF NODES

Using
statistical arguments, Einstein showed that light is
not a mere wave, but comes in photons as he called energy quanta,
multiples of
Planck’s constant h. Regrettably Einstein conceived of the photon
as a point particle containing all of its energy like a spinning billiard ball,
similar to
the then recently discovered electron. This single supposition
alone is
responsible for all the conceptual troubles that have plagued (QM) ever
since.
Now de-Broglie and Schrödinger had a wave-particle duality to deal with
when trying
to explain how a particle of mass m can have a wave-like frequency: a
wave of
what? Born’s introduction of the probability function, avoided
the necessity
of finding a physically realistic answer to all these new questions. A
‘particle’
such as the photon was assumed to have a probability of being anywhere
until it
was detected, when it ‘collapsed’ in one position only. Quantum
weirdness was
born.

The Compton Effect[66] has been widely interpreted as experimental proof that the photon can act like a particle. Recent work however shows that a wave interpretation is equally valid [95]. In (BU) the reason for the particle-wave duality becomes
clear: The photon
starts out with the ordered release of energy from all the nodes making
up
electrons surrounding the nucleus, creating a pattern of energy
transfer that
has both forward and radial momentum. It spreads thereafter from node
to node
as an electromagnetic wave-like pattern. The photon is always a wave pattern
made up of particle-like nodes. There is no need to puzzle over
an
elusive duality that shows up according to how the photon is observed.

2.7 (BU)
EXPLAINS QUANTUM PROBABILITY AND THE
UNCERTAINTY RELATIONS

Tamari[22], [67]
has shown that a classical dipole’s far- field spreads as a bow-wave
that
contains both forward and radial momentum from which the basic elements
of QM
and GR can be derived directly and simply (FIG.28).

FIG. 28 The
static and
time- harmonic Electric field component parallel to the dipole’s z axis
on any
line -AA normal to that axis follows the form of a Gaussian probability
distribution, providing a physical interpretation of the quantum
probability
wave function. The value for j was chosen to fit the probability curve
to Ez of
the field of a simple dipole, for z=B=100.

The
components of the electric field of any cross-section
of the dipole field normal to the dipole axis closely resemble a normal
distribution, i.e. a probability function. Another way to see how the
pattern
of node interactions can be studied probabilistically based on an FCC
lattice
is shown in (FIG. 29 a.) Each node transfers its energy to
the 13 immediately
adjacent nodes in the FCC lattice. Had each node interacted with only
two
nodes, a binomial probability distribution would have resulted (FIG. 29
b.) With
13 nodes in each branch of the tree the normal distribution is reached
rapidly
as the energy spreads in the lattice.

FIG. 29
Diffusion of
energy between nodes creates a normal distribution resembling
probability. (a)
In an actual 3 Dimensional FCC lattice momentum arriving at a given
node A is
transferred to nine neighboring nodes. (b) In a 2-D lattice the
energy from A
is transferred as a binomial distribution, so that the energy levels of
the top
row of nodes lie on a probabilistic normal curve P.

Heisenberg
used diffraction blurring the image in a
microscope as an example of his uncertainty relations.10 In
Tamari’s
united dipole paper22 the uncertainty relations, for example
between
momentum direction and position, emerge from this physical dipole model
simply
and naturally: the photon wave starts out from a single node but can
diffract
in all directions (albeit at discrete angles which get finer as the
wave
spreads far in the network). Far away from the source, the photon is
now a wave
of energy spread over a wide area, but with the node orientation
concentrated mostly
in the forward direction (FIG. 30).

FIG. 30.
Heisenberg’s Uncertainty
Relations are a direct consequence of the geometry of a diffracting,
i.e. an expanding
dipole wave. The momentum range is indirectly proportional to the width of
the wave x measured either along a streamline S or an
equipotential surface of
the field. A (BU) node rotating through pi in one second, by
definition, is half a unit of action (h).

This
model adapts itself easily in (BU), but instead of a
single dipole with a classical wave spreading in vacuum, the bow wave
radiates via
a field of other dipoles.

It
now becomes possible to think that the wave function solutions
of Schrödinger’s equation 9describe the angular momentum
pattern of nodes
oscillating in a standing-wave pattern. This is something that has yet
to be proved
rigorously, but is made plausible because this wave equation contains
the
constant (h), which in (BU) is the unit of angular momentum for each
node. On
the other hand, the infinite number of plane-wave Fourier components
making up
Heisenberg’s matrices[68] now has a physical explanation from the lattice geometry of (BU):
Considering
the lattice packing as a crystal, a straight lines radiating from a
node A to B
can have a plane orthogonal to it containing a number of nodes. The
orientation
of each of these planes can be adapted from its Miller index, a
convention used
to define facet angles in crystals[69].
The infinity of such lines that can radiate from A, each at a unique
orientation
constitutes the plane wave components of the matrix (FIG. 31).

FIG. 31.
Heisenberg’s
matrices have been interpreted as the infinite plane waves of the
Fourier
components of a wave. A 2D (a) and 3D (b), (c) interpretation of this
concept
in (BU) theory. The planes are considered as crystal-like facets, i.e.
planes
intercepting the lattice at different angles . These planes are defined by their Miller
indices
which are the intercepts of the plane on the x, y, and z
coordinates .

2.8
QUANTUM ENTANGLEMENT IS LOCAL AND CAUSAL
IN (BU)

In (BU) the photon is a wave-like
pattern of energy states within the fixed nodes of the lattice, and not
a point
particle, making it unnecessary to use imaginary ‘probability
waves’. Of
course there are genuinely random physical processes in nature, for
example in
the timing, phase or polarization involved in the emission and
absorption of incoherent
photons. These are the end result of complex and chaotic interactions
which are
in themselves linear, local and causal.

In (BU) a causal, local and
physically realistic explanation of quantum effects banishes the whole
range of
conceptual mysteries, weirdness or magic that have plagued (QM) for
most of the
past century. From the point of view of (BU) theory, Einstein and
his colleagues
posed the wrong challenge to (QM) in their ‘EPR Paradox’ paper[70]:
The authors questioned how mutually
random spins of the entangled pair of electrons arriving at distant
locations, can
have any correlation between them outside the light cone allowed by
(SR), assuming
that only local interactions are possible. Bell’s Theorem[71] and Clauser’s experiments[72],
using photon polarization as a
variable, successfully challenged this view: there is a
correlation
although there were no signals exchanged between the distant photons
prior to
or after their alleged ‘collapse’ when they were sensed. What
should have been
questioned in the EPR paper instead was the (QM) notion that an
electron’s spin
(or a photon’s polarization) direction is inherently random in all
possible
circumstances.

In (BU) all of these suppositions
reduce to this simple scenario: the two photons emitted by the
same atom start
out in opposite directions having identical polarization, which is
retained intact
when they arrive at the sensors at their respective distant locations.
They are
entangled because they are identical from start to finish. Their
polarization
states are faithfully transmitted from node to node across the network,
and
when the sensor data is compared, of course their polarization states
are
highly correlated. There is no need to conjure either ‘spooky’
instantaneous
action-at-a-distance[73] or hidden variables[74] to explain what is happening. All the interactions are causal and
local, as is
everything else in (BU). There is no need to appeal to scenarios
involving
backwards travel in time[75],
multiple universes[76],
or mental processes in the mind of the observer[77] to explain why the photon ‘chooses’
one path or the other.

Something quite similar is
involved when trying to explain the double-slit interference
experiments.
Again, the photons and particles involved are not imbued with a
supernatural
sense that can tell if the other photon or particle has passed through
a
particular slit or not. In (BU) either one of two scenarios
applies: In the
case of radiation, the wave always passes through both slits at
once and
different parts of the wave front interfere with each other, just as in
a
water-ripple experiment. This explains how faint-light single-photons
produce
this interference effect[78],
although in the sensing screen individual atoms with random
states accumulate the radiation randomly until a quanta is absorbed, giving the
impression of
point-like photons arriving there to make up the pattern. Dirac’s
maxim that
‘a photon interferes only with itself’[79] has a clear physical explanation in the context of (BU).

Double-slit interference experiments involving
particles such as electrons or protons require another
explanation: the
particle has an electrostatic or gravitational field, it is speculated
that in (BU)
the particle passes through one slit, while it’s accompanying
gravitational or
electrostatic waves pass through the other slit. The particle arrives
at the
sensor and interferes with its own field arriving there at the same
time (FIG.
32).

FIG 32. Double-slit
interference for
radiation and particles in (BU). (a) A plane wave-front approaches the
screen
and passes simultaneously from the two slits, interfering at the sensor
at the
top. (b) A particle passes through the slit to the right while
its own
gravitational waves diffracts through the other slit. The particle and
its own
gravity interfere at the sensor.